Problem: Kevin is 2 times as old as Vanessa. 28 years ago, Kevin was 6 times as old as Vanessa. How old is Vanessa now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Vanessa. Let Kevin's current age be $k$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $k = 2v$ 28 years ago, Kevin was $k - 28$ years old, and Vanessa was $v - 28$ years old. The information in the second sentence can be expressed in the following equation: $k - 28 = 6(v - 28)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = 2v$ . Substituting this into our second equation, we get: $2v$ $-$ $28 = 6(v - 28)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $2 v - 28 = 6 v - 168$ Solving for $v$ , we get: $4 v = 140.$ $v = 35$.